Uniqueness of solutions for a mathematical model for magneto-viscoelastic flows

Abstract

We investigate uniqueness of weak solutions for a system of partial differential equations capturing behavior of magnetoelastic materials. This system couples the Navier-Stokes equations with evolutionary equations for the deformation gradient and for the magnetization obtained from a special case of the micromagnetic energy. It turns out that the conditions on uniqueness coincide with those for the well-known Navier-Stokes equations in bounded domains: weak solutions are unique in two spatial dimensions, and weak solutions satisfying the Prodi-Serrin conditions are unique among all weak solutions in three dimensions. That is, we obtain the so-called weak-strong uniqueness result in three spatial dimensions.

References in corpus (2)

• Weak-strong uniqueness for measure-valued solutions of some compressible fluid models
• Existence of weak solutions to an evolutionary model for magnetoelasticity

Cited by in corpus (1)

• Weak-strong uniqueness of renormalized solutions to reaction-cross-diffusion systems